Download D-modules, representation theory, and quantum groups: by Louis Boutet de Monvel, C. De Concini, C. Procesi PDF

By Louis Boutet de Monvel, C. De Concini, C. Procesi

Lectures Given on the second consultation of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Venezia, Italy, June 12-20, 1992

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Extra info for D-modules, representation theory, and quantum groups: lectures given at the 2nd session of the Centro internazionale matematico estivo

Sample text

Gr" M]z, associ~ au prerfiier terme de cette suite. /T* V) (modulo l'agrandissement Z " C Z~). I1 reste encore s comparer s l'~l~ment cette image K-th~orique et celle du th~or~me. I1 est assez facile de voir que [M]z a m~me image K-th~orique dans Kz,(T*X) que sa "d~formation au c6ne tangent" [gr v g r M ] c z , off CZ C H x v T * X / Y d~signe le c6ne tangent de Z le long de H; il reste alors s montrer que les 61~ments [grgr ~ M] et [gr ~ g r M ] ont la mfime image K-th6orique dans Kz,(T*X). Ce dernier point n'est pas 6vident parce qu'il met en jeu deux filtrations dont la comparaison n'est pas imm6diate.

2 Let us recall that a category C consists in giving: i) A class of elements, called the objects. ii) For each pairs of objects A, B a set home(A, B) of elements called morphisms. iii) For any 3 objects A, B, C a composition of morphisms: homc( A, B) x home(B, C) ---* home(A, C) These data are subject to the following simple axioms: a) Composition is associative whenever defined. b) For every object A there is a morphism 1A E home(A, A) which behaves as a unit element under compositions: 1Af = f and glA = g, when defined.

Series, Princeton University Press 144 (1951). Verdier J. , Categories d~riv~es, ~tat 0, SGA 489 vol. , 1977, pp. 262-311. Q U A N T U M GROUPS C. S Pisa, C. Procesi Univ. di Roma INDEX Chapter 1 Hopf algebras w Hopf Algebras Categories, functors etc. ~2 Complete reducibility Chapter 2 Finite dimensional representations w w w w Finite dimensional representations of algebras and filtrations Twisted derivations and polynomial algebras Representation theory of twisted derivation algebras Representation theory of twisted polynomial rings Chapter 3 Quantum groups w w w w Some properties of finite root systems Quantum groups Degenerations of quantum groups Poisson structures Chapter 4 The Poisson group H w w w w w w w The quantum group A A universal construction associated to the braid group B as functions on a Poisson group Some Hamiltonian fields The geometry of the quantum coadjoint action Verma modules The center Chapter 5 Roots of 1 w w w w Frobeniusmap Baby Vermamodulesand the degree The center ofUe.

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